The present invention relates to a method and apparatus for estimating PSK modulated signals such as BPSK, QPSK and DQPSK modulated signals, that is, for measuring or estimating the modulation accuracy of modulators which are used to generate these modulated signals, and an apparatus for detecting origin offsets of vectors composed of in-phase and quadrature-phase signals in the base-bands of these PSK modulated signals.
A conventional modulated signal estimating apparatus is disclosed in, for example, Raymond A. Birgenheier, "Measuring the Modulation Accuracy of .pi./4 DQPSK Signals for Digital Cellular Transmitters," Hewlett-Packard Journal, Vol. 42, No. 2, pp 73-82, April 1991 or U.S. Pat. No. 5,187,719 issued Feb. 16, 1993. A brief description will be given, with reference to FIG. 1, of this prior art modulated signal estimating apparatus. A DQPSK modulated signal, provided as an intermediate frequency signal to an input terminal 10, is converted by an analog-to-digital (A/D) converter 11 to digital data, which is fed via an intermediate frequency band-pass filter 12 to a burst detector 13, whereby only a signal portion is extracted. The thus extracted signal is applied to an interpolation filter 14 and a Hilbert transformer 15. The Hilbert transformer 15 produces, as its output, a quadrature component of the input signal thereto, and the quadrature component is fed to an interpolation filter 16. The output from the burst detector 13 is also applied to a baud rate phase detector 17, which detects a baud rate, that is, a phase difference .tau. between the center point of a symbol in the input modulated signal and a symbol clock used to determine the symbol. The phase difference .tau. is used to compensate the interpolation filters 14 and 16 which are FIR filters, for instance; their weight coefficients or functions are corrected in accordance with a deviation of an impulse response from an impulse train which is produced by unit delay arrays of the filters 14 and 16, that is, in accordance with the baud rate phase.
The in-phase component and the quadrature component output from the interpolation filters 14 and 16, respectively, are fed to adders 18 and 19, wherein in-phase and quadrature components of an I-Q origin offset are subtracted from them to obtain an in-phase component I(k) and a quadrature component Q(k). The component I(k) and Q(k) thus obtained are provided to an amplitude and phase detecting part 21, which computes an instantaneous amplitude a(k)=.sqroot.I(k).sup.2 +Q(k).sup.2 and an instantaneous phase .theta.(k)=tan.sup.-1 {Q(k)/I(k)} of a vector which are dependent on the in-phase and quadrature components. The instantaneous amplitude a(k) and the instantaneous phase .theta.(k) are fed to a parameter calculating part 22, and the instantaneous phase .theta.(k) is provided to a data detector 23 as well, wherein .theta.(k)-.theta.(k-5) calculated. In this example, k represents one data sample point, and one signal sampling period is selected to be equal to one-fifth of the symbol interval. Therefore, one symbol interval is equal to five sampling periods. That is, in this example, the in-phase component I(k) and the quadrature component Q(k) are provided every one-fifth of the symbol interval, and hence the instantaneous amplitude and the instantaneous phase are calculated every one-fifth interval of the symbol; the data detector 23 detects the difference between the current instantaneous phase and the instantaneous phase one symbol interval before, and the detected phase difference is used to estimate an ideal symbol of the modulated signal in a symbol generator 24. That is, the symbol generator 24 generates symbols "0, 0" for a phase difference 0.degree. to 90.degree., "0 1" for 90.degree. to 180.degree., "1, 0" for -9.degree. to 0.degree. and "1, 1" for -180.degree. to -90.degree., respectively. The symbols thus obtained are correlated with a unique 28-bit synchronization word in a synchronizer 25 to establish the word interval. The output from the synchronizer 25 is fed to a reference signal generating part 26, which generates a reference instantaneous amplitude .theta..sub.r (k) and a reference instantaneous phase .theta..sub.r (k) corresponding to the ideal reference vector, dependent on the estimated symbols, and provides them to the parameter estimator or calculating part 22.
The parameter calculating part 22 calculates values of parameters A.sub.0, .sigma..sub.0 and .OMEGA..sub.0 that minimize a linear approximation expression of the square mean value of an error vector given by the following equation (1). EQU .epsilon..sup.2 =.SIGMA.a(k)a.sub.r (k)exp(.sigma..sub.o k){[1nA.sub.o +.sigma..sub.o k+1na(k)-1na.sub.r (k)].sup.2 +[.theta.(k)-.theta..sub.r (k)-.OMEGA..sub.0 k-.theta..sub.0 ].sup.2 } (1)
In the above, the parameter A.sub.0 is a transmitter gain, .sigma..sub.0 is a droop factor (an amplitude variation per symbol), .OMEGA..sub.0 is an offset frequency (a phase variation per symbol) and .theta..sub.0 is a phase error. These parameters are used to calculate an in-phase component I.sub.0 and a quadrature component Q.sub.0 of an I-Q origin offset B.sub.0 by the following equations (2) and (3). EQU I.sub.0 =(1/N).SIGMA.{A.sub.0 a(k)exp(.sigma..sub.o k)cos [.theta.(k)-.OMEGA..sub.0 k-.theta..sub.o ]-a.sub.r (k)cos .theta..sub.r (k)} (2) EQU Q.sub.0 =(1/N).SIGMA.{A.sub.0 a(k)exp(.sigma..sub.0 k)sin[.theta.(k)-.OMEGA..sub.0 k.theta..sub.0 ]-a.sub.r (k)sin .theta..sub.r (k)} (3)
In the equations (2) and (3), .SIGMA. is from k=0 to N-1 and N is the number of decided symbols.
In the event that the I-Q origin offsets I.sub.0 and Q.sub.0 thus calculated are larger than a threshold value, they are multiplied by (1/A.sub.0)exp{-.sigma..sub.0 k+j(.OMEGA..sub.0 k+.theta..sub.0) in a multiplier 36. The in-phase component (a real part) is subtracted by the adder 18 from the output of the interpolation filter 14, and the quadrature component is subtracted by the adder from the output of the interpolation filter 16. The outputs from the adders 18 and 19 are individually processed as the in-phase component I(k) and the quadrature component Q(k) in the same fashion as described previously, and the equations (1) through (3) are performed by the parameter calculating part 22. Thereafter, the same process as mentioned above is repeated until it is decided in a decision part 27 that the I-Q origin offset B.sub.0 is smaller than the threshold value.
When the origin offsets I.sub.0 and Q.sub.0 become smaller than the threshold values as the result of such a repetition of the calculations, the parameters A.sub.0, .sigma..sub.0 and .OMEGA..sub.0 obtained at that time in the parameter calculating part 22 are provided to a local carrier oscillator 28, which generates a local carrier signal A.sub.0 exp{.sigma..sub.0 k-j[.OMEGA..sub.1 .OMEGA..sub.0)k+.theta..sub.0 ]} dependent on the parameters, where .OMEGA..sub.1 is the frequency of the intermediate frequency signal to the input terminal 10. A sine-wave and a cosine-wave signal from the local carrier oscillator 28 are multiplied by the output from the interpolation filter 14 in multipliers 29 and 31, that is, the input DQPSK signal undergoes an orthogonal detection. The outputs from the multipliers 29 and 31 are fed to adders 32 and 33, wherein the in-phase component Re(B.sub.0)=I.sub.0 and the quadrature component Im(B.sub.0)=Q.sub.0 of the I-Q origin offset obtained in the parameter calculating part 22 are subtracted from the above-mentioned multiplier outputs. The outputs from the adders 32 and 33 are passed through low-pass filters (square root raised cosine filters) 34 and 35 to obtain a modulated signal of the transmitted signal (the input signal), that is, in-phase and quadrature components of the baseband signal. The in-phase component I(k) and the quadrature component Q(k) are provided to the amplitude and phase detecting part 21, whereby an instantaneous amplitude and an instantaneous phase are detected as described previously. Furthermore, the difference in the instantaneous phase every symbol interval is detected and a symbol is estimated. An ideal reference instantaneous amplitude and an ideal reference instantaneous phase corresponding to the estimated symbol are produced and provided to the parameter calculating part 22. Moreover, the instantaneous amplitude and the instantaneous phase detected by the amplitude and phase detecting part 21 are also supplied to the parameter calculating part 22, wherein various parameters are calculated as referred to previously. Where the thus obtained parameters differ from those produced previously, the above operation is repeated.
In this way, refined parameters are decided and are used to again control the local carrier oscillator 28, and the sine-wave and cosine-wave signals from the local carrier oscillator 28 are fed to the multipliers 29 and 31 and multiplied by the outputs from the interpolation filters 14 and 16, respectively, whereby the in-phase and quadrature components are detected. A difference between the vector composed of such detected in-phase and quadrature components and an ideal reference vector Sr(k)=Ar(k)exp{j.theta..sub.r (k)} from the reference signal generating part 26 is calculated in an error vector calculating part 39 and a mean value of the error vector is calculated. The mean value represents the modulation accuracy. That is, it is the modulation accuracy that is obtained by averaging the error vector 38 between a detected vector 36 [A.sub.0 exp{.sigma..sub.0 k-j(.OMEGA..sub.0 k+.theta..sub.0)}Z(k)] compensated in timing, amplitude, frequency, phase and dc offset with respect to the vector Z(k) of the baseband signal of the input modulated signal and an ideal reference vector 37 {Sr(k)} on an I-Q plane coordinates as shown in FIG. 2. The modulation accuracy thus obtained and the parameters .OMEGA..sub.0, .sigma..sub.0, I.sub.0 and Q.sub.0 calculated by the parameter calculating part 22 are displayed on a display 40.
FIG. 3 shows the signal processing procedure of the traditional modulation accuracy estimating apparatus described above. In step S1 the equation (1) is computed by the least squares method using the linear approximation on the assumption that the I-Q origin offset B.sub.0 is zero. The resulting parameters A.sub.0, .sigma..sub.0, .theta..sub.0 and .OMEGA..sub.0 are used to calculate the equations (2) and (3) to obtain the I-Q origin offset B.sub.0 (S2). If the I-Q origin offset B.sub.0 thus obtained is smaller than the threshold value (S3), and if larger than the threshold value, the I-Q origin offset is multiplied by (1/A.sub.0)exp(-.sigma..sub.0 k+j(.OMEGA..sub.0 k+.theta..sub.0)) (S4), and the multiplied output is used to correct the outputs from the interpolation filters 14 and 16 (S5). The same steps as mentioned above are repeated for the corrected result, and they are repeated until the I-Q origin offset B.sub.0 becomes smaller than the threshold value. When the I-Q origin offset B.sub.0 becomes smaller than the threshold value, coherent demodulation, that is, the same operation as demodulation in an ordinary receiver is conducted (S6). Conventionally, the I-Q origin offset B.sub.0 is assumed to be zero at first and the parameters are estimated by linear approximation as described above, hence it is necessary to repeat the calculations until correct parameters are obtained. Thus, the processing time is inevitably long and, in some cases, optimal results cannot be obtained even after repeating the calculations.
It is therefore an object of the present invention to provide a PSK modulated signal estimating method and apparatus which permit measurement of the modulation accuracy in a shorter time than in the prior art.
Another object of the present invention is to provide a PSK modulated signal estimating method and apparatus which permit measurement of the modulation accuracy in a shorter time than in the prior art even if the frequency difference between the input modulated signal and the local carrier is relatively large.